Effective Annual Rate

\[EAR=\left(1+\frac{r}{m}\right)^m-1\]

Variables

EAReffective annual rate (decimal)

rnominal annual interest rate (decimal)

mcompounding periods per year

Description

What is this formula?

The Effective Annual Rate (EAR) calculates the true annual interest rate earned or paid after accounting for compounding during the year.

Unlike a nominal interest rate, the EAR reflects the actual growth of money resulting from periodic compounding.

When to use it

Use this formula when comparing loans, investments, savings accounts, bonds, or financial products that compound interest multiple times per year.

Example

Suppose:

Nominal Annual Rate = 12% = 0.12

Compounding Frequency = 12 times per year

Formula:

EAR=(1+r/m)^m−1

Substitution:

EAR=(1+0.12/12)^12−1

EAR=(1.01)^12−1

EAR=0.126825

Result:

Effective Annual Rate = 12.68%

Applications

Loan comparison

Investment analysis

Savings accounts

Banking products

Financial planning

Corporate finance

Note

The Effective Annual Rate assumes a constant nominal rate and a fixed compounding frequency. Real financial products may include fees, taxes, changing rates, or special conditions that cause the actual return to differ from the calculated EAR.